This paper proposes an augmented Lagrange Hopfield network (ALHN) for combined heat and power economic dispatch (CHPED) problem. The ALHN method is the continuous Hopfield neural network with its energy function based on augmented Lagrangian relaxation. In the proposed ALHN, the energy function is augmented by Hopfield terms from Hopfield neural network and penalty factors from augmented Lagran...

In this work, we propose a two-way coupling technique between total Lagrangian smoothed particle hydrodynamics (SPH) method for Solid Mechanics and the explicit incompressible SPH (EISPH) to simulate fluid–structure interaction problems. solid part, framework guarantees that distribution keep stable correctly calculate deformation gradient thus elastic forces. The constitutive model follows hyp...

Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with the extended Lagrangian framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dyna...

In a typical video rate allocation problem, the objective is to optimally distribute a source rate budget among a set of (in)dependently coded data units to minimize the total distortion of all units. Conventional Lagrangian approaches convert the lone rate constraint to a linear rate penalty scaled by a multiplier in the objective, resulting in a simpler unconstrained formulation. However, the...

This paper proposes an augmented Lagrangian Hopfield network (ALHN) for combined heat and power economic dispatch (CHPED) problem. The ALHN is the continuous Hopfield neural network based on augmented Lagrangian relaxation as its energy function. In the proposed ALHN, its energy function is augmented by Hopfield terms from Hopfield neural network and penalty factors from augmented Lagrangian re...

Using the notion of vacuum pairs we show how the (square of the) mass matrix of the fermions can be considered geometrically as curvature. This curvature together with the curvature of space-time, defines the total curvature of the Clifford module bundle representing a “free” fermion within the geometrical setup of spontaneously broken Yang-Mills-Higgs gauge theories. The geometrical frame disc...

Based on the classic augmented Lagrangian multiplier method, we propose, analyze and test an algorithm for solving a class of equality-constrained nonsmooth optimization problems (chiefly but not necessarily convex programs) with a particular structure. The algorithm effectively combines an alternating direction technique with a nonmonotone line search to minimize the augmented Lagrangian funct...

We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic odd-intrinsic-parity sector at order p6. The Lagrangian contains 24 in principle measurable terms and no contact terms for the general case of Nf light flavours, 23 terms for three and 5 for two flavours. In the two flavour case we need a total of 13 terms if an external singlet vector field is included. ...

We design a fast ascent direction algorithm for the Lagrangian dual problem of the single-machine scheduling problem of minimizing total weighted completion time subject to precedence constraints. We show that designing such an algorithm is relatively simple if a scheduling problem is formulated in terms of the job completion times rather than as an 0-1 linear program. Also, we show that upon t...